Atmospheric oscillations-III

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The theory of the oscillations of a planetary atmosphere, developed in earlier papers, is extended to the case of a perturbation arising from Hall conductivity. An explicit form is obtained for the system matrix, and the sub-matrix LX2L, which determines the horizontal modal structure in the separable case, is shown to be Hermitian. The orthogonal eigenmodes of the latter are computed for zonal oscillations in a dipole magnetic field; they are qualitatively similar to Hough modes, but significant errors in equivalent depth and angular distribution will arise if an averaging procedure is used to convert the region to an equivalent Coriolis region. The horizontal modes of semi-diurnal oscillation are computed for a uniform Hall region of a rotating atmosphere, and are interpreted in terms of an isothermal model of the E-region; a critical value of \¯ghH~ 1 exists, beyond which negative modes become increasingly important in the description of low-l motion, with an associated increase in reflection of tidal energy. A more detailed model of the E-region, taking into account the vertical variation of temperature and conductivity, and also the effects of Pedersen conductivity, will be considered later.

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